A method in an Optical Line Terminal (OLT) device for transmitting a flow control message to an Optical Network Unit/Terminal (ONU/T) device in a Passive Optical Network (PON) access network is provided. The OLT device is configured to receive alarm and/or Attribute Value Change (AVC) messages from the ONU/T device. The OLT device is also configured to temporarily store the alarm and/or AVC messages in a message queue. The OLT device generates a flow control message indicating that the ONU/T device is to stop transmitting alarm and/or AVC messages to the OLT device, when the number of alarm and/or AVC messages in the message queue exceeds a first threshold. Then, the OLT device transmits the flow control message to the ONU/T device(s). An OLT device for transmitting a flow control message to an ONU/T device, and an ONU/T device and related method for receiving a flow control message are also provided.